Sunday, August 10, 2014

It's The Population, Stupid

The Times of India recently reported,
not without a certain self-congratulatory air, that: "The latest wealth
index by New World Wealth that looks at multimillionaires — an individual with
net assets of at least $10 million — has ranked India eighth in the global rich
list, below countries such as the US, China, Germany and the UK but above
Singapore and Canada."

This has certainly sent Indian cyberspace into a little tizzy. A
common celebratory headline: "India has more multimillionaires than
Australia, Russia and France!” And given that the
largest number of the world’s poor also live in India, a common admonitory
reaction is: "See? Told you so! India is just a corrupt society."

This isn't the first time we've been gobsmacked by the sort of
numbers India can generate. Recently, farmer suicides did the rounds, with the
already large numbers (around 300,000 since 1995) helped along by the Indian
numbering system: read here for why some participants in a recent BBC debate had it wrong by a factor of
10 . All quite understandable: India is so large that nobody has a real
sense of the numbers anyway. Which is why the following handy little motto should
always be clutched close to heart and brain:

When confronted by a Large Indian Statistic, consider dividing by
the population.

We learn from the same source (New World Wealth) that the
world has 495,000 multimillionaires, and India has 14,800 of them. Divide:
India has just 3% of the world's multimillionaires. It has, however, 17% of the
world's people. Suddenly India is looking like it does not have its “fair
share” of multimillionaires.

Now, of course, India is a poorer country. The real question is
whether India has more than its expected share of multimillionaires once we
take into account this fact. To do this in a lot of detail will take some real
work, but we’re in a back-of-the-envelope mood for this post. So, whipping out a handy envelope on World
Bank letterhead, we carry out some quick calculations.

In 2012 Indian per-capita income was USD 1,550, and world per-capita
income around USD 10,235, suggesting that the ratio of Indian per-capita income to
the world average is a measly 0.15. Meanwhile, the multimillionaire ratio (India’s
share relative to its population) is 3/17 = 0.17. These two ratios are very
close, which suggests that neither self-congratulation nor admonition is quite
called for at this stage. But we will need to dig deeper.

Let’s think about millionaires for a moment: those
with assets of USD 1m or more. According to WealthInsight (see
this link), India had 251,000 millionaires
in 2012, around 0.02% of the population. The corresponding number for the
United States is 5,231,000, around 1.64%. Thus, using the United States
as a benchmark, India’s millionaire share in the population relative to the US
is 1.22% (the ratio of 0.02 to 1.64). At the same time,
India’s per capita income is 3% of that of the US. So: does India have too few millionaires relative to the
United States, after making the income correction? Not really: if two countries
have the same level of relative inequality but different mean incomes, a
halving of mean income predicts a change in the population incidence of
(multi)millionaires by a factor that typically comes down by more than half, the exact prediction depending on the
distribution of wealth. This is (in part) because “millionaire” or “multimillionaire”
is a threshold concept: a fixed
monetary figure (USD1m for the former, USD10m for the latter) has to be
crossed. One good way to explore the predicted change
is to employ a Pareto distribution of wealth, along with the
population-weighted average Gini coefficient for wealth distributions (which is
a bit over 0.65, and calculated from this link). Then a halving
of per-capita income is expected to lower the (multi)millionaire share of the
population by a factor of approximately 2.38. If we really go out on that limb
and plummet from the heights of US per-capita income (USD 50,660) to that of
India (USD 1,550), we would expect the both the millionaire share and the
multimillionaire share in India to be approximately 1.28% that of the United
States.

Since the actual millionaire share in India relative
to the United States is 1.22%, which is remarkably close to the prediction, India does not appear to be out of line, as far as millionaires are concerned (and after we
have corrected for economic differences). But the case of multimillionaires tells a rather different story. In India the multimillionaire
share is 0.001% of the population, while in the United States it is 0.058%.
Taking ratios, we see that the multimillionaire
share in the population in India is 2.06% of the corresponding share in the
United States. This number is surely high relative to
the prediction of 1.28%.

This parallels findings by Piketty and
his colleagues. India does not stand out in terms of income going to the top
1%, but it does in terms of income going to the top 0.1%.While there is noise in all these data, we
would tentatively conclude that India, controlling for economic differences,
has “more multimillionaires than it should.” While this may generate
applause in some circles, we would therefore side with the
admonitory warning bell sounded by Raghuram Rajan.

Country

Relative Income

M-Share

MM-Share

Predicted

Relative Share

Relative M-Share

Relative MM-Share

India

0.03

0.020

0.001

1.28

1.22

2.06

China

0.11

0.094

0.002

6.54

5.71

3.38

Hong Kong

0.72

2.604

0.213

65.88

158.56

370.25

UK

0.75

1.053

0.034

70.08

64.12

58.76

Germany

0.88

1.643

0.031

85.44

100.03

54.62

Japan

0.94

1.656

0.017

92.73

100.85

28.68

US

1.00

1.642

0.058

100.00

100.00

100.00

Singapore

1.01

2.908

0.122

101.06

177.07

212.20

Switzerland

1.60

3.639

0.224

179.66

221.61

389.25

World

0.20

0.167

0.007

13.54

10.18

11.97

Notes and
Sources: Relative
Income is country per-capita income relative to US per-capita income (from
the World Bank Databank). M-Share is
millionaire divided by population, in percent, and MM-Share is multimillionaire divided by population, in percent
(from Times of India, New World Wealth, WealthInsight, and United Nations). Predicted Relative Share uses Relative
Income and a Pareto distribution, along with the population-weighted average of
within-country wealth Ginis (approx. 0.67) to generate predicted relative share
of millionaires and multimillionaires in each country relative to the United
States, in percent.Relative M-Shareand Relative
MM-Share are the actual relative shares generated from columns 3 and 4, by
expressing those numbers relative to the US numbers, in percent.

Remembering that the United States is itself a country with very
high inequality, this is additional cause for concern.For instance, China comes in below its predicted value for both
millionaires and multimillionaires, and countries such as Japan and Germany
come in far below the predictions for multimillionaires, as does the world as a
whole. Countries with a significantly higher share than their predicted values
are Hong Kong, Singapore and Switzerland; see Table.

Take away points? India
is poorer than the world average and so naturally has a greater percentage of
poor people and a lower percentage of rich people. Yet using the absolute
numbers, India has more of almost everything, which is misleading. Indeed,
correcting for income differences, India has the “expected share” of
millionaires relative to the United States. However, looking at the super-rich,
namely, the multi-millionaires, India does have more than its expected share:
something not too savory is cooking on the very end of the right tail.

Lesson: for India, always do the percentages, whether
for multimillionaires or for farmer suicides. We might then learn something.

Endnote: A previous version of this post contained a cautionary endnote explaining that our rudimentary analysis could be complicated by a proper accounting of threshold effects. Following up on this, we subsequently extended the analysis.